Fully exploiting soft robots' capabilities requires devising strategies that can accurately control their movements with the limited amount of control sources available. This task is challenging for reasons including the hard-to-model dynamics, the system's underactuation, and the need of using a prominent feedforward control action to preserve the soft and safe robot behavior. To tackle this challenge, this letter proposes a purely feedforward iterative learning control algorithm that refines the torque action by leveraging both the knowledge of the model and data obtained from past experience. After presenting a 3D polynomial description of soft robots, we study their intrinsic properties, e.g., input-to-state stability, and we prove the convergence of the controller coping with locally Lipschitz nonlinearities. Finally, we validate the proposed approach through simulations and experiments involving multiple systems, trajectories, and in the case of external disturbances and model mismatches.